Topics in discrete mathematics 1

2022/2023
Programme:
Mathematics, Second Cycle
Year:
1 ali 2 year
Semester:
first or second
Kind:
optional
Group:
M2
ECTS:
6
Language:
slovenian, english
Hours per week – 1. or 2. semester:
Lectures
2
Seminar
1
Tutorial
2
Lab
0
Content (Syllabus outline)

The lecturer selects some important topics in discrete mathematics, such as: Partially ordered sets. Ramsey theory. Matroids. Discrete geometry. Designs and configurations. Symmetric graphs. Symmetries of combinatorial objects. Symmetric functions. Combinatorial enumeration. Discrete probability. Metric graph theory. Domination theory. The Tower of Hanoi problem.
Special care should be taken to minimize overlap with other courses in this program.

Readings

Jack H. van Lint, Robin J. Wilson: A Course in Combinatorics, Cambridge University Press, Cambridge, 2001.
R. L. Graham, M. Grötschel and L. Lovász, editors: Handbook of Combinatorics, Elsevier Science B.V., Amsterdam, MIT Press, Cambridge, MA, 1995
Predavatelj poleg tega lahko izbere tudi primerne novejše raziskovalne članke iz znanstvenih revij.

Objectives and competences

Students encounter some of the important areas of discrete mathematics, such as partially ordered sets, discrete geometry, discrete probability, partitions, and symmetric functions.With individual presentations and team work interactions within seminar/project activities students acquire communication and social competences for successful team work and knowledge transfer.

Intended learning outcomes

Knowledge and understanding: Students get acquainted with the subject matter, the methods, and the main results of various areas of discrete mathematics.Application: Students will be able to use their knowledge in different mathematical and other contexts.Reflection: Students comprehend the interplay and mutual enrichment of various areas of discrete mathematics.Transferable skills: Students learn methods which are useful in construction and analysis of discrete mathematical models.

Learning and teaching methods

Lectures, exercises, homeworks, consultations

Assessment

Type (examination, oral, coursework, project):

Exercise-based exam (2 midterm exams instead of written exam, written exam or homework)
Theoretical knowledge exam (oral exam)

Grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

Sandi Klavžar:
KLAVŽAR, Sandi. Structure of Fibonacci cubes: a survey. Journal of combinatorial optimization, ISSN 1382-6905, 2013, vol. 25, iss. 4, str. 505-522. [COBISS-SI-ID 16603737]
KLAVŽAR, Sandi, SHPECTOROV, Sergey. Convex excess in partial cubes. Journal of graph theory, ISSN 0364-9024, 2012, vol. 69, no. 4, str. 356-369. [COBISS-SI-ID 16243033]
HAMMACK, Richard H., IMRICH, Wilfried, KLAVŽAR, Sandi. Handbook of product graphs, (Discrete mathematics and its applications). Boca Raton, London, New York: CRC Press, cop. 2011. XVIII, 518 str., ilustr. ISBN 978-1-4398-1304-1. [COBISS-SI-ID 15916121]
Matjaž Konvalinka:
KONVALINKA, Matjaž, PAK, Igor. Non-commutative extensions of the MacMahon Master Theorem. Advances in mathematics, ISSN 0001-8708, 2007, vol. 216, no. 1, str. 29-61. [COBISS-SI-ID 15545689]
KONVALINKA, Matjaž. Divisibility of generalized Catalan numbers. Journal of combinatorial theory. Series A, ISSN 0097-3165, 2007, vol. 114, iss. 6, str. 1089-1100. [COBISS-SI-ID 14354265]
KONVALINKA, Matjaž, PAK, Igor. Triangulations of Cayley and Tutte polytopes. Advances in mathematics, ISSN 0001-8708, 2013, vol. 245, str. 1-33. [COBISS-SI-ID 16706905]
Primož Potočnik:
POTOČNIK, Primož. Tetravalent arc-transitive locally-Klein graphs with long consistent cycles. European journal of combinatorics, ISSN 0195-6698, 2014, vol. 36, str. 270-281. [COBISS-SI-ID 16862041]
POTOČNIK, Primož, SPIGA, Pablo, VERRET, Gabriel. Cubic vertex-transitive graphs on up to 1280 vertices. Journal of symbolic computation, ISSN 0747-7171, 2013, vol. 50, str. 465-477. [COBISS-SI-ID 16520537]
POTOČNIK, Primož. Edge-colourings of cubic graphs admitting a solvable vertex-transitive group of automorphisms. Journal of combinatorial theory. Series B, ISSN 0095-8956, 2004, vol. 91, no. 2, str. 289-300. [COBISS-SI-ID 13087321]
Riste Škrekovski:
GOVORČIN, Jelena, KNOR, Martin, ŠKREKOVSKI, Riste. Line graph operation and small worlds. Information processing letters, ISSN 0020-0190. [Print ed.], 2013, vol. 113, iss. 5-6, str. 196-200. [COBISS-SI-ID 16561497]
DVOŘÁK, Zdeněk, LIDICKÝ, Bernard, ŠKREKOVSKI, Riste. Randić index and the diameter of a graph. European journal of combinatorics, ISSN 0195-6698, 2011, vol. 32, iss. 3, str. 434-442. [COBISS-SI-ID 17410905]
KAISER, Tomáš, STEHLÍK, Matěj, ŠKREKOVSKI, Riste. On the 2-resonance of fullerenes. SIAM journal on discrete mathematics, ISSN 0895-4801, 2011, vol. 25, no. 4, str. 1737-1745. [COBISS-SI-ID 16244569]